We investigate the weakening of elastic materials through randomly
distributed circles and cracks numerically and compare the results to
predictions from homogenization theories. We find a good agreement for the case
of randomly oriented cracks of equal length in an isotropic plane-strain medium
for lower crack densities; for higher densities the material is weaker than
predicted due to precursors of percolation. For a parallel alignment of cracks,
where percolation does not occur, we analytically predict a power law decay of
the effective elastic constants for high crack densities, and confirm this
result numerically.Comment: 8 page